Russia has accused the US of trying to start a new Cold War after Congress passed a law banning Russians linked to serious human rights abuses from entering America.

Moscow furiously claimed that the new law, which also bars blacklisted Russians from owning US land and using the banking system, was evidence of a "vindictive desire" to damage Russia's world standing.

"Apparently, Washington has forgotten what year this is and still thinks the Cold War is going on," the Russian foreign ministry said on its official Twitter account. It added that the move would "adversely affect the prospects of bilateral cooperation" between the two powers.

Sergei Lavrov, the foreign minister, later said Russia would respond by introducing its own visa ban for US human rights abuses.

“At my meeting with Hillary Clinton in Dublin I confirmed that we will deny entry [to Russia] to Americans who are certainly involved in human rights violations,” he said after meeting the US Secretary of State and Lakhdar Brahimi, the UN and Arab League envoy to Syria, in Ireland on Thursday.

The so-called Magnitsky Law prompted calls from British critics of Russia for similar action from the Government, amid concerns about the death of an exiled Russian in Surrey. Alexander Perepilichnyy had been assisting a criminal inquiry prompted by the whistleblowing lawyer whom the new US law is named after.

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The American law was approved overwhelmingly by the US Senate last night as part of a raft of measures primarily aimed at restoring normal trade relations between Russia and America.

The package replaced a 38-year-old Act that imposed trade sanctions on the Soviet Union for not allowing Jewish Russians and other persecuted minorities to emigrate from the Communist bloc.

The human rights law was named after Sergei Magnitsky, a Russian lawyer who died in a Moscow prison in 2009 after exposing an alleged $230 million (£143 million) tax fraud by Russian police and officials.

Mr Magnitsky, who was working for an American-Russian law firm, claimed to have been tortured. He died after almost a year in custody, a week before he would have had to be released or face trial.

The measure was proposed by John McCain, the veteran Republican senator for Arizona and former presidential candidate. Mr McCain said last night that he was "sending a signal to Vladimir Putin and the Russian plutocracy that these kinds of abuses of human rights will not be tolerated".

Orrin Hatch, a Republican senator for Utah, added after the 92-4 vote: "We should respond to Russia's continued corruption and human rights violations".

Russia was last night mulling retaliation. Alexei Pushkov, the head of the foreign affairs committee in the Duma, the lower chamber of parliament, said similar sanctions could be imposed on US officials linked to human rights abuses.

"It is perplexing and preposterous to hear human rights complaints from the US, where torture and kidnapping are legal in the 21st century," the Russian foreign ministry added in its Twitter onslaught.

Mr Perepilichny, 44, collapsed and died suddenly near his home on an upmarket, heavily protected estate in Surrey on November 10. Police have been struggling to establish the cause of his death.

He had moved to Britain three years ago and had been helping Swiss prosecutors investigate a Russian criminal group suspected of being involved in the widespread fraud exposed by Mr Magnitsky.

A group of senior MPs, including former foreign secretaries David Miliband and Sir Malcolm Rifkind, have been pushing the Government to make official a similar "Magnitsky blacklist" in Britain.

Dominic Raab, a Conservative member of the group, has said Mr Magnitsky was part of a "noble Russian tradition of dissidents who stood up for the rule of law, democratic reform and free speech."

President Barack Obama had hoped to prevent yesterday's passage of the new human rights law, in an effort to avoid enraging Moscow. He insisted that he was already empowered to blacklist Russian human rights abusers by executive order.

Ignoring the Magnitsky measure, Mr Obama last night welcomed the new trade agreement. He said in a statement that he hoped to "ensure that American businesses and workers are able to take full advantage".

It was reported in September that Theresa May, the Home Secretary, had quietly sent a list of 60 Russian officials implicated in the corruption case uncovered by Mr Magnitsky, and to his death in custody, to the Russian embassy in London, banning them from entering Britain.

Government spokesmen declined to confirm the report but said that ministers would not allow foreigners against whom there was evidence of human rights abuses of entering the country.

MPs passed a motion earlier this year calling on ministers to implement a British equivalent of the new US law. However it is believed that Foreign Office officials, also fearing provocation of Mr Putin and the Russian government, are stubbornly blocking any measure that would require the public release of a "blacklist" of banned Russians.